Negative refraction of acoustic waves in two-dimensional phononic crystals has been demonstrated through both analysis and exact numerical simulation. The methods to achieve this behavior have been discussed. A microsuperlens for acoustic waves has also been designed. It is shown that refractive devices based on phononic crystals behave in a manner similar to that of optical systems. Therefore, a negative square root of the effective density or negative refraction index for acoustic waves can be introduced to describe this phenomena very well as the case of electromagnetic waves in the photonic crystals.